
Linear Equation
Find the general solution of the given differential equations, the largest interval over which the solution is defied and determine whether there are any transient terms in the solution.
I mainly need someone to check my answer and if they're wrong to help me correct the mistakes I made
$\displaystyle dy/dx  2y = x^2 + 5$
I found the integrating factor to be $\displaystyle e^^2^x$
Multiplied both sides by integrating factor and integrated to get:
$\displaystyle e^^2^xy = 1/2x^2e^^2^x  1/2xe^^2^x  5/2e^^2^x + C$
$\displaystyle y = x^2/2  x/2  5/2 + Ce^2^x$
Largest interval I think would be (∞, ∞) and I don't think there are any transient terms
Thanks in advance.

Check your answers by differentiating and plugging into the DE and see if it satisfies the DE. What do you get?